Continuous Wave (“CW”) Light detection and ranging (“Lidar”) is a sensing technology using light waves to determine a distance to objects. Radio detection and ranging (“Radar”) is a sensing technology using radio waves to determine a distance to objects. Sound Navigation and Ranging (“Sonar”) is a sensing technology using sound waves to determine a distance to objects. In CW Lidar, Radar, or Sonar systems, a wide band signal (e.g., light, radio, or sound waves, respectively), may be transmitted toward an object and the signal reflecting off that object may be received by the CW Lidar, Radar, or Sonar system. The received signal may be correlated with the digitized received signal and converted into a pulse through a mathematical transformation. One method for determining the correlation is described in Equation 1:
                              R          ⁡                      (                          ref              ,              data                        )                          =                                            1              N                        ⁢                                          ∑                                  m                  =                  0                                                  N                  -                  1                                            ⁢                                                          ⁢                                                                    ref                    *                                    ⁡                                      (                    m                    )                                                  ⁢                                  data                  ⁡                                      (                                          m                      +                      n                                        )                                                                                =                                    DFT                              -                1                                      ⁡                          (                                                                    DFT                    *                                    ⁡                                      (                                          ref                      *                                        )                                                  ⁢                                  DFT                  ⁡                                      (                    data                    )                                                              )                                                          (        1        )            
In Equation 1, “*” denotes the complex conjugate, N is the number of modulation repeats, ref is the reference signal and data is the digitized received signal from the receiver of the CW Lidar, Radar, or Sonar system. Typically, the complex quadrature from may be used for the reference and this would consist of the repeating wideband signal, such as linear swept frequency or some other signal. The position of the peak of this pulse may determine how far away the object is and the precision of the measurement depends on the sample rate.
Limitations in the hardware of the some conventional CW Lidar, Radar, or Sonar systems may limit the sampling rate, and therefore the data resolution may also be limited. For example, hardware limitations may limit the sample rate such that only a 75 meter data resolution may be achieved. However, 3 meters of data resolution may be needed for certain measurements, such as atmospheric CO2 column measurements with a CW Lidar. Various current types of interpolation can be applied to the data from conventional CW Lidar, Radar, or Sonar systems, but current types of interpolation can take too long and can require too many resources to be implemented in a real time application. What is needed is a viable method for providing high-speed interpolated fine resolution range measurements.